The game got underway following a minute's silence in memory of former Benetton player Piero Dotto, who died on Thursday.
Ruaridh Jackson missed an early penalty as heavy rain made handling difficult for both sides, but it wasn't long before the Warriors' fly-half notched his first points of the evening.
Penalties on 12 and 15 minutes put Glasgow into a 6-0 lead, but that was wiped out when Treviso kicked a penalty to touch and from the resulting lineout No. 8 Manoa Vosawai was driven over the line for the first try of the night.
Kris Burton added the extras to make it 7-6 to Treviso and a subsequent penalty after Glasgow were penalised at the scrum sent the home side in at the break with a four-point advantage.
Gregor Townsend's men were sharper after the restart with Jackson reducing the deficit with a penalty on 44 minutes. Scott Wright replaced Jackson shortly after and a 56th-minute penalty put Glasgow back in front.
The momentum seemed to be with Glasgow but a yellow card for replacement Tim Swinson for pulling down a drive gave Tobias Botes a shot at goal and he didn't waste it to give Treviso a one-point advantage.
But from a scrum deep in the Italian's 22 the scrum-half's pass into midfield failed to find a player and Seymour gleefully nipped in to prod the ball over the line and dive on it, with the try awarded by the TMO after it appeared to cross the dead-ball line.
Wight added the extras to make it 19-13 with 14 minutes remaining and then with Glasgow attacking produced a peach of a cross-field kick that Treviso failed to deal with, allowing Seymour to score his second of the night unopposed from close range with the officials missing an apparent knock-on in the build-up.
Although Wight missed the conversion, Swinson returned from the sin-bin to bolster the Glasgow defence and despite another yellow card late on for Ofa Fainga'anuku they held on for victory to ensure they stay third in the RaboDirect PRO12 table.
|Benetton Treviso Score Card|
|Glasgow Warriors Score Card|